Compressibility of lime-treated dredged slurry with high water content

Lime is widely used for soft ground treatment, rendering the compressibility of lime-treated soil a crucial factor in deformation analysis in engineering applications. This study investigated the compressibility of three remoulded lime-treated slurries with high water content in Southeast China. Sixty groups of oedometer tests were conducted on lime-treated soils with an initial water content of 1 to 3 times the liquid limit and lime contents between 1 and 3%. The oedometer test results were discussed to examine the remoulded yield stress \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upsigma }_{y}^{\prime}$$\end{document}σy′ of lime-treated slurry. Considering the relationships between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upsigma }_{y}^{\prime}$$\end{document}σy′, the void ratio, lime content, and initial water content were preliminarily discussed and quantitatively established. Research on the normalised compression curve of lime-treated soil revealed that for soil samples containing a lime content of 0–%, the normalised compression curve at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upsigma }_{p}^{\prime}$$\end{document}σp′>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upsigma }_{y}^{\prime}$$\end{document}σy′ can be represented by a unique line. Furthermore, the log(1 + e) − log \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma }_{\text{v}}^{\prime}$$\end{document}σv′ compression curve of lime-treated slurry at pre-yield state is analysed, and a prediction method for the modified compression index is proposed.


Soil
The study used three distinct types of soil samples, as follows: (1) Wenzhou slurry was obtained from a sea reclamation region in Dongtou County, Wenzhou.The geological context is as follows: The soil layer ranging from − 1.34 to 0.83 m primarily consists of dredged slurry with an initial water content exceeding 100%.(2) Taizhou slurry, acquired from a reclamation site formed through the deposition of soils dredged from Luqiao district, Taizhou.The soil sample originates from the dredged slurry layer (− 6.47 m to 2.41 m).(3) Hangzhou slurry, extracted from a foundation pit at a construction site in Shangcheng District, Hangzhou.The soil sample was obtained from the silt layer (− 1.99 m to − 0.85 m).
Table 1 summarises the physical properties of the three slurries.The w L (liquid limit) of Hangzhou and Taizhou slurry is similar, whereas that of Wenzhou slurry is higher.According to Casagrande's plasticity chart (Fig. 1), the data point of Wenzhou slurry is located below the A-line defined by PI = 0.73 × (w L − 20).This indicates that Wenzhou slurry belongs to the high plasticity silt group.Similarly, the Taizhou and Hangzhou slurries can be classified as silt with low plasticity, using the Unified Soil Classification System (USCS).Figure 2 and Table 2 display the XRD (X-Ray Diffraction) and XRF (X-Ray Fluorescence) experimental results for three types of slurry samples.The experimental results indicate that the mineral composition of the three slurry samples is primarily dominated by primary minerals, with a relatively uniform mineral composition.Quartz has the highest content, followed by kaolinite and illite.The Wenzhou slurry also contains a certain amount of mica, while the Taizhou slurry includes minor amounts of calcite and albite.
Table 1.Basic physical properties of the three slurries.USCS refers to a unified soil classification system; ML refers to silt with low plasticity; MH refers to silt with high plasticity.

Experimental apparatus
The initial effective vertical stress in the standard consolidation tests is 12.5 kPa in accordance with the standard for the soil test method (ASTM D2435-2011).However, the dredged slurry with a high water content used in this test (water content up to three times the liquid limit) was not sufficiently rigid to endure such a large vertical stress.Therefore, a modified oedometer apparatus with an initial effective vertical stress of 1 kPa was used to conduct the oedometer test of the high water content lime-treated soil.This modified oedometer apparatus was equipped with a light loading cap and two weight hanger systems, as shown in Fig. 3. Information on the device is detailed in Hong and colleagues 15 .The soil samples had a diameter of 6.18 cm and a height of 2 cm.When the effective vertical pressure ranged from 0 to 12.5 kPa, the sample was loaded using the first set of loading systems, positioned at the center point of the consolidation cell.However, when the vertical pressure exceeded 12.5 kPa, the sample was loaded using the second set of loading systems, which could provide higher vertical pressures.The samples were loaded in the following sequence: 1 kPa, 2 kPa, 3 kPa, 4 kPa, 6 kPa, 8 kPa, 10 kPa, 12.5 kPa, 25 kPa, 50 kPa, 100 kPa, 200 kPa, 300 kPa, 400 kPa, and 800 kPa.Each loading process lasted for approximately 24 h.

Sample preparation
The soil sample used in this test was first air-dried and then passed through a target sieve (D max = 0.4 mm) to remove large impurity particles.All the samples were prepared using the same procedure.A dosage of hydrated lime (designated as 0%, 1%, 2%, and 3% by dry weight of soil) was applied.The soil powder was thoroughly mixed with lime and humidified using distilled water.The initial water content of specimens was adjusted within the range of 1.0-3.0times their liquid limits (designated as 1.0, 1.5, 2.0, 2.5, and 3.0 times their liquid limits, respectively).Table 3 presents the variable sets for the total of sixty tests.The homogeneous mixture was subsequently transferred to the oedometer rings.After placement in the rings, the soil samples with w 0 = 1.0-1.5

Compression curve
The selection of the compression relationship had a significant influence on the analysis of soil compression characteristics.The e-log σ ′ v compression relationship is the most frequently used approach for normally consolidated soils.The compression curve of normally consolidated soil is often approximated as either a straight line or a curve with only one knee point in e-log σ ′ v coordinates.For this type of soil sample, the Casagrande method can be used to derive the preconsolidation pressure or yield stress.
Figure 4 reflects the e-log σ ′ v curves of Wenzhou natural soil samples under various water content conditions.It is evident that for soft clays with high water content, a distinct straight line is not discernible towards the end of the e-log σ ′ v curve.Instead, the overall compression curve assumes an inverted "S" shape, particularly when the water content lies between 100 and 250% 19 .Therefore, the Casagrande method cannot be used to determine the yield stress of soils characterised by high water content.
Butterfield 12 first introduced the bilogarithmic method for interpreting oedometer test data for natural soils.The compression curves of lime treated soil can be effectively represented by two straight lines on a plot of log (1 + e) against log σ ′ v .The effective vertical stress σ ′ v at the intersection point of these two straight lines is the remoulded yield stress ( σ ′ y ).Several researchers, including Onitsuka and colleagues 20 , Sridharan and Prakash 21 , Hong and Onitsuka 22 , and Hong 23 , have validated the accuracy of the proposed method.They demonstrated that the oedometer test data of reconstituted clays could also be plotted as a straight line in the bilogarithmic graph, if the applied vertical stress exceeds σ ′ y .Consequently, similar to the interpretation approach for natural soils, the oedometer test data for the reconstituted clays can be represented by two straight lines in the bilogarithmic graph.Figures 5, 6, 7, and 8 exhibit the logarithmic compression curves of the three remoulded slurries with varying lime content.It is observed that most of the oedometer test data can be adequately represented by two straight lines in the log (1 + e) − log σ ′ v coordinate, except for soil samples with a 0% lime content and a water content of three times the liquid limit.These exception cases can be approximated by a straight line.The stress values at the intersection of the two straight lines correspond to the yield stress.The left straight line corresponds to the pre-consolidation state when σ ′ v < σ ′ y , whereas the right straight line correspond to the post-consolidation state line when where the vertical effective stress is less than the yield stress, the compressibility of the sample is relatively low.Once the vertical effective stress surpasses the yield stress, a significant increase in compressibility is observed, to the extent that the compression modulus may exceed that of untreated samples.The compressibility of lime-treated soil increases with the addition of lime content and decreases with an increase in moisture content.

Remolded yield stress
Table 4 lists the yield stresses of the three soil samples, each with varying lime and water contents.The test results showed that soil's yield stress increased with an increase in lime content, whereas it decreased with an increase in water content.This phenomenon can be attributed to the ion-exchange reaction between the calcium ions in www.nature.com/scientificreports/ the calcium hydroxide and the sodium ions on the soil particle surface that occurred after the lime was mixed into the soil sample.Ion exchange reduces the thickness of the double-electron layer on the surface of the soil particles, prompting their agglomeration into floccules.With the long-term action of lime, a pozzolanic reaction between excess lime and soil particles produces calcium silicate hydrate (CSH), and calcium aluminate hydrate (CAH) gels with lower water content, which further enhances the strength of the soil.However, an increase in soil water content reduces the concentration of calcium ions and affects the alkaline environment inside the lime-treated soil, resulting in a decrease in the lime treatment effect.Existing data also suggest that soil water content may affect the lime modification optimum (LMO) of soil.The reinforcing effect of lime treatment on soil does not indefinitely increase with increasing lime content but begins to decrease slowly beyond a threshold value.This threshold value, called the lime modification optimum, was first introduced by McCallister and Petry 20 through their leaching tests conducted on lime-treated clay.Using the Hangzhou soil sample as an example, when the lime content increases from 1 to 2%, the yield stress of the samples with varying water contents increased by 22.0%, 54.6%, 116.3%, 176.6%, and 205.5%, respectively.This observation highlights that with increasing water content, the effect of lime treatment on the remodelled yield stress becomes evident.
Furthermore, the influence of lime content on the remoulded yield stress was analysed.When the lime content was increased further (3%), the increase in remoulded yield stress decreased significantly.This indicates that the optimal lime content of the Hangzhou slurry is 2%.However, for the remaining samples, the lime content needs to be further increased to determine the optimal lime content.

Statistical analysis of remolded yield stress
Hong 23 showed that the void ratio at the liquid limit ( e L ) can serve as an index for standardising the relation- ships between the initial void ratio e 0 and yield stress for various reconstituted clays.According to Hong's www.nature.com/scientificreports/investigation 19 , a unique relationship between yield stress and e 0 /e L was established for remoulded clay samples with initial water content in the range of 0.7-2.0 times the liquid limit.The following formula was used to describe this relationship: When σ ′ y is the remoulded yield stress, e 0 is the initial void ratio, e L is the void ratio at liquid limit and σ yL is the yield stress for various reconstituted soils at their liquid limits.
In this study, this formula was used to analyse the relationship between the yield stresses and pore ratio of the three silts.The results revealed that this formula yielded a good fitting effect on the silts as well.Regression analysis yielded the following simple equation with a correlation coefficient R 2 of 0.966 (Fig. 9): The value of σ yL in this formula is 8.31 kPa, which surpasses the value reported by Hong 19 .The rationale for this discrepancy is that the soil sample used in this study was silt and had a substantially higher sand content (particle diameter greater than 0.075 mm) than the soil sample used in Hong 19 .The friction angle of the sample increases as the proportion of sand particles rises, ultimately increasing the pre-consolidation of the soil 24 .
Previous research has shown that lime treatment exerts a significant influence on the plasticity index of soil.The soil's liquid limit rises with increasing lime content 25 .This can probably be attributed to the substitution of Ca 2+ with Na + and K + in clay minerals, leading to a reduction in the soil water content 26 .To capture the effect of the lime treatment on the intrinsic properties of a given soil, the parameter L was introduced in the empirical formula, which represents the effect of the lime treatment on the soil's intrinsic properties such as soil strength, plasticity index, and void ratio at the liquid limit: (1) where σ ′ y is the yield stress of the lime-treated soil, e ′ 0 is the initial void ratio of the lime-treated soil.The parameter σ yL , set at 8.31, represents the yield stress of the initial soil sample at the liquid-limit void ratio.The fitting formula was as follows: The yield stress of the lime-treated soils with different water contents was fitted.The fitting results are shown in Fig. 10.The new formula fits better the yield stress of lime-treated soil, and the correlation coefficients of the fitting formula for the 1%, 2%, and 3% lime contents are 0.963, 0.941, and 0.984, respectively.

Sampling location
Lime content 1.0-time liquid limit 1.5 times liquid limit 2.0 times liquid limit 2.5 times liquid limit  Based on the void index, Burland 14 introduced a normalised compression curve termed the intrinsic compression line (ICL).Hong and colleagues 15 researched the intrinsic compression line of remoulded soil characterised by high water content and proposed an EICL to clarify the compression properties under high water content.EICL refers to the extended intrinsic compression line, which extends the ICL of Burland 14 to an effective vertical stress as low as 1.5 kPa.Hong and colleagues 15 suggested that the EICL should be used for the remoulded soil with w L = 28-100% and w 0 = 0.7-2.2w L .
This paper analysed the EICL of three kinds of remoulded silt with w L = 38-56% and w 0 = 1.0-3.0w L over the stress range from the remoulded yield stress to 800 kPa.And the expression is: where σ ′ v is vertical effective stress.Figure 11 shows the relationship between the void index and effective vertical stress for the three types of remoulded soil and compares the normalised compression curves in this study with ICL and EICL.The line in this study is almost identical to the EICL proposed by Hong 15 , and is located above the ICL.
Figures 12 and 13 depict the correlation between the void index and vertical effective stress for lime-treated slurry across varying initial water and lime contents.The I v -log σ ′ v compression curve of lime-treated soil is similar to that of remoulded soil.The compression curve of the lime-treated slurry with higher initial water content aligns beneath the curve representing lower water content.Beyond a vertical effective of 50 kPa, I v -log σ ′ v compression curves for lime-treated slurry with different water content tend to normalise into a line, which is similar to the findings of Burland 14 and Hong 19 .With an increase in lime content, the void index of the limetreated slurry decrease under lower vertical stress conditions.However, when the vertical effective stress surpasses a certain threshold, the I v -p curves tended to be consistent across different lime contents.
Figure 14 shows the normalised compression curve of the lime-treated slurries with varying lime contents over the stress range from the remoulded yield stress ( σ ′ y ) to 800 kPa.The normalised compression curves for the lime-treated slurries with 1%, 2%, and 3% lime content are as follows: The squares of the correlation coefficient (R2) are both above 0.99.A detailed analysis of the normalised compression curves of the lime-treated slurries with varying lime contents showed that the three curves were essentially consistent (Fig. 15).Consequently, a unified analysis of the compression curves of slurry samples with under various conditions (soil samples: Wenzhou soil, Hangzhou soil, Taizhou soil; initial moisture content: 56%, 84%, 112%, 140%, 168%; lime content: 1%, 2%, 3%) was performed, and a normalised compression curve of high water content slurry suitable for 1-3% lime content was obtained.( 6)

Void index
Effective vertical stress (kPa) The normalised compression curve aptly characterises the compressibility of lime-treated slurry when σ ′ v > σ ′ y .However, it is essential to highlight that the compression curves of lime-treated slurries when σ ′ v < σ ′ y cannot be normalised into a unique line.Because the remoulded yield stress increased significantly following the lime treatment, the normalised compression curves are not able to portray the compressibility exclusively of the limetreated slurry.Therefore, it is imperative to analyse the compression curve of lime-treated slurry when σ ′ v < σ ′ y , and propose a simple method to predict the compression curve at the pre-yield state.
In this study, bilogarithmic compression curves were used to analyse the compressibility of lime-treated slurries.The log(1 + e) − log σ ′ v compression model is expressed as follows: where C cr is the modified compression index, that is, the slope of the straight-line segment of the log(1 + e) − log σ ′ v compression model.Figure 3 shows that the log(1 + e) − log σ ′ v compression curve of lime-treated soil is composed of two straight lines.This section primarily analyses the straight-line segment when σ ′ v < σ ′ y .The slope of this section is expressed as C cr1 .Table 5 lists the C cr1 values of the Wenzhou slurry for varying lime and initial water contents.The C cr1 of the lime-treated slurry increased with increasing initial water content and decreased with increasing lime content.
We further analysed the relationship between C cr1 and the soil parameters.It is widely accepted that the value of C cr1 is directly related to the degree of the cementation bond, as reflected by σ ′ y 27,28 .Normalised parameters σ ′ y /(e 0 /e L ) were used in this study to analyse the C cr1 of the lime-treated slurry.Figure 16 shows the relationship between σ ′ y /(e 0 /e L ) and C cr1 , which can be expressed as:

Validation
In order to validate the I v -p curves of lime-treated soil obtained in the present work, additional test data were compared with the formula.The oedometer test data of five soil samples are taken from previous studies [29][30][31][32] .
The basic properties of the soil samples used in the validation test are shown in Table 6.
Figure 17      www.nature.com/scientificreports/curves of lime-treated soil derived in the article successfully predict the compression characteristics of the samples with lime content ranging from 0 to 3%.

Conclusion
The findings of 60 groups of oedometer tests for a lime treated high-water-content slurry in Southeast China are presented in this paper.The compression curve of the slurry was measured in the pressure range of 1-800 kPa and its yield stress was analysed.
Using the log(1 + e) − log σ ′ v compression relationship to analyse the soil's compression curve it is evident that lime treatment promotes the formation of a stable soil structure in the soil and imparts the yield stress to the clay soils.The yield stress of the lime-treated soil increased with an increase in lime content and significantly decreased with an increase in water content.Further analysis of the yield stress revealed that the optimal lime content of the soil varied significantly with the water content.
Based on the regression equation of yield stress σ ′ y and normalised parameters e 0 /e L proposed by Hong 19 , this paper presents an empirical formula suitable for lime-treated soil and an empirical parameter L reflecting the effect of lime treatment.The new formula combines the yield stress of lime-treated soil with the original remodelled soil parameters to obtain a good fit.
A normalised compression curve for lime-treated slurry with 1% to 3% lime content was established, and a simple method was proposed to predict the modified compression index of lime-treated slurry in pre-yield state.Based on this, the preliminary evaluation of compression characteristics of lime-treated slurry can be conducted without oedometer testing.
Burland14 proposed a normalising index, the void index I v , to normalise the compression curves of remoulded clay.The expression for the void index I v is where e * 100 and e * 1000 are the porosity index of the remodelled silt when the vertical effective stress is 100 kPa and 1000 kPa, respectively; C * c is called the inherent compression index, equal to ( e * 100 − e * 1000 ).
shows a comparison between the I v -p curves of lime-treated soil and the validation results.The results indicate that the oedometer test outcomes for the five samples align well with the fitted curves.The I v -p (11) C cr1 = 0.043 σ ′ y /(e 0 /e L ) −0.523 0.043(σ σ ' y /(e 0 /e L )) -0.523

Figure 17 .
Figure 17.Comparison between verification results and I v -p curves of lime-treated soil.

Table 2 .
Chemical composition of three slurries.

Table 3 .
. Initial water content and lime content of three slurries.

Initial water content, w 0 : % Liquid limit, w L : % w 0 / w L Lime content: %
L were soaked under water and then subjected to vacuum for 24 h to facilitate saturation.This vacuum time is typically considered adequate to eliminate the effect of suction on compression.Soil samples exhibiting high water content in the fluid state were considered to be saturated.Subsequently, the sample was cured at 22 ℃ for 28 d following saturation.It should be noted that the soil sample remained immersed in water during the curing process. w

Compressibility of lime-treated slurry at pre-yield state
Figure 11.Comparison of normalised compress curves with ICL and EICL.Vol:.(1234567890)

Table 5 .
. The C cr1 values of Wenzhou slurry after lime treatment.

Table 6 .
. Basic physical properties of test samples.